Higher Asymptotics of Laplace's Approximation
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Submission date: 09. Oct. 2008
published in: Asymptotic analysis, 70 (2010) 3/4, p. 231-248
DOI number (of the published article): 10.3233/ASY-2010-1016
MSC-Numbers: 41A60, 41A63, 44A10
Keywords and phrases: Laplace's approximation, Laplace integral, asytmptotic expansion
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We present an explicit asymptotic series for multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the integrand.